A254333 Squares (A000290) which are also centered pentagonal numbers (A005891).

1, 16, 1156, 22801, 1666681, 32878756, 2403352576, 47411143081, 3465632747641, 68366835443776, 4997440018745476, 98584929298781641, 7206305041398228481, 142159399682007682276, 10391486872256226723856, 204993755756525779060081, 14984516863488437537571601

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..634

Index entries for linear recurrences with constant coefficients, signature (1,1442,-1442,-1,1).

Formula

a(n) = a(n-1)+1442*a(n-2)-1442*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+15*x^3-302*x^2+15*x+1) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)).

Example

16 is in the sequence because it is the 4th square number and the 3rd centered pentagonal number.

Mathematica

LinearRecurrence[{1, 1442, -1442, -1, 1}, {1, 16, 1156, 22801, 1666681}, 20] (* Harvey P. Dale, Jul 26 2015 *)

Prog

(PARI) Vec(-x*(x^4+15*x^3-302*x^2+15*x+1) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))

Crossrefs

Cf. A000290, A005891, A129557, A254332.

Sequence in context: A279295 A353029 A053903 * A102807 A373453 A160131

Adjacent sequences: A254330 A254331 A254332 * A254334 A254335 A254336

Keyword

nonn,easy

Author

Colin Barker, Jan 28 2015

Status

approved